arXiv subjects
Publications and source records attributed to Richard Warnung.
We pick up the regime switching model for asset returns introduced by Rogers and Zhang. The calibration involves various markets including implied volatility in order to gain additional predictive power. We focus on the calculation of risk measures by Fourier methods that have successfully been applied to option pricing and analyze the accuracy of the results.
In practice daily volatility of portfolio returns is transformed to longer holding periods by multiplying by the square-root of time which assumes that returns are not serially correlated. Under this assumption this procedure of scaling can also be applied to contributions to volatility of the assets in the portfolio. Close prices are often used to calculate the profit and loss of a portfolio. Trading at exchanges located in distant time zones this can lead to significant serial cross-correlations of the closing-time returns of the assets in the portfolio. These serial correlations cause the square-root-of-time rule to fail. Moreover volatility contributions in this setting turn out to be misleading due to non-synchronous correlations. We address this issue and provide alternative procedures for scaling volatility and calculating risk contributions for arbitrary holding periods.
In this article we consider a Brownian motion with drift of the form \[dS_t=μ_t dt+dB_t\qquadfor t\ge0,\] with a specific nontrivial $(μ_t)_{t\geq0}$, predictable with respect to $\mathbb{F}^B$, the natural filtration of the Brownian motion $B=(B_t)_{t\ge0}$. We construct a process $H=(H_t)_{t\ge0}$, also predictable with respect to $\mathbb{F}^B$, such that $((H\cdot S)_t)_{t\ge 0}$ is a Brownian motion in its own filtration. Furthermore, for any $δ>0$, we refine this construction such that the drift $(μ_t)_{t\ge0}$ only takes values in $]μ-δ,μ+δ[$, for fixed $μ>0$.